Let's understand the meanings of the following phrasal verbs:
Get back: to return to a place after you have been somewhere else.
Get up: to stand up.
Get over (something): to accept an unpleasant fact or situation after dealing with it for a while.
Get away: to leave or escape from a person or place, often when it is difficult to do this.
Get on: have a good relationship.
People have come to the field from their jobs to buy the lottery. So, after buying the lottery they would go back to their workplaces. Filling the blank with 'back' gives a similar meaning.
No other phrasal verb makes the sentence correct.
Hence, option a) is correct.
Note: Phrasal verb: A phrase that consists of a verb with a preposition or adverb or both, the meaning of which is different from the meaning of its separate parts. Example: She has always looked down on me. Here, the phrasal verb 'to look down on someone' doesn't mean that you are looking down from a higher place at someone who is below you; it means that you think that you are better than someone.